The least number, which when divided by 5, 6, 7 and 8 leaves

Home » Aptitude » Number System » Question

The least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case, but when divided by 9 leaves no remainder, is :

1. 1677
2. 1683
3. 2523
4. 3363

Correct Option: B

Firstly, we find LCM of 5, 6, 7 and 8.

⇒ LCM = 2 × 5 × 4 × 3 × 7= 840
Required number = 840x + 3 which is exactly divisible by 9.
Now, 840p + 3 = 93p × 9 + 3p + 3
When p = 2 then 840p + 3, is divisible by 9.
∴ Required number = 840 × 2 + 3 = 1683